Development of Integrated Choice and Latent Variable (ICLV) Models Using Matrix-Based Analytic Approximation and Automatic Differentiation Methods on TensorFlow Platform

Table 3

Simulation results for the three-alternative ICLV model.

Parm.	True value	Parameter estimates			Standard error estimates
		Mean est.	Abs. bias	APB (%)	ASE	FSSD	R. eff
	0.5	0.5300	0.0300	5.9924	0.0961	0.0807	1.1908
	0.6	0.6411	0.0411	6.8506	0.1177	0.1003	1.1730
	0.5	0.5022	0.0022	0.4432	0.2037	0.1493	1.3648
	0.6	0.6017	0.0017	0.2775	0.2451	0.1845	1.3288
	0.3	0.3125	0.0125	4.1630	0.0408	0.0466	0.8740
	0.3	0.3027	0.0027	0.9119	0.1336	0.1118	1.1950
	−0.4	−0.4061	0.0061	1.5186	0.1773	0.1455	1.2182
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.6855	0.0855	14.2485	0.2567	0.2516	1.0206
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.6230	0.0230	3.8411	0.4800	0.3951	1.2149
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	−1	−1.0013	0.0013	0.1312	0.0366	0.0334	1.0974
	−1	−1.0244	0.0244	2.4418	0.0680	0.0638	1.0664
	−1	−1.0031	0.0031	0.3117	0.0441	0.0453	0.9720
	−1	−1.0665	0.0665	6.6513	0.1629	0.1609	1.0124
	0.3	0.2880	0.0120	3.9911	0.0508	0.0441	1.1524
	0.4	0.4459	0.0459	11.4847	0.1550	0.1355	1.1441
	0.5	0.4924	0.0076	1.5296	0.0754	0.0832	0.9064
	0.6	0.7157	0.1157	19.2758	0.3046	0.2619	1.1633
	1.5	1.4971	0.0030	0.1967	0.0275	0.0265	1.0375
	1.5	1.5354	0.0354	2.3578	0.0873	0.0823	1.0601
	1.5	1.4949	0.0051	0.3431	0.0504	0.0549	0.9191
	1.5	1.6141	0.1141	7.6054	0.2346	0.2114	1.1101
	0.5	0.4863	0.0137	2.7409	0.0954	0.0888	1.0741
	−1	−0.9972	0.0028	0.2784	0.1360	0.1530	0.8893
	−1	−0.9980	0.0020	0.1971	0.0419	0.0434	0.9667
	−0.8	−0.7978	0.0022	0.2772	0.0338	0.0343	0.9852
	0.5	0.4807	0.0193	3.8694	0.0885	0.0811	1.0907
	0.2	0.2129	0.0129	6.4477	0.0661	0.0517	1.2771
	0.5	0.4929	0.0071	1.4146	0.0718	0.0723	0.9929
	0.2	0.2112	0.0112	5.6136	0.0622	0.0543	1.1441
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0.6	0.6065	0.0065	1.0794	0.1374	0.1196	1.1483
	1.36	1.3753	0.0153	1.1286	0.2742	0.2571	1.0668
Overall mean value			0.0236	3.7940	0.1308	0.1169	1.1190

Note: “--” indicates that the corresponding parameter is fixed at the true value.